I think you have mixed up "normal" and "natural." Something can be natural but not normal. For example, a solar eclipse is natural; it is not a normal occurrence.

:point:

It’s called a normal distribution — T Clark

:point: :point:

It’s within one standard deviation of the mean — T Clark

Maybe the idea of compossibility is relevant to this discussion. Wikipedia describes compossibility as follows:

"According to Leibniz, a complete individual thing (for example a person) is characterized by all its properties, and these determine its relations with other individuals. The existence of one individual may negate the possibility of the existence of another. A possible world is made up of individuals that are compossible—that is, individuals that can exist together."

So it seems the existence of Nixon with a different possible set of properties would be not compossible with the same Nixon with other actual properties in a given possible world; they could not both exist therein. But one of them can exist therein.

Notice that "both" Nixons would be different "individuals" by Leibniz's definition even though each refers to the same person as that person is rigidly defined.

Again, I think the key is that Nixon's other properties are just possible properties and that being the case, there is no contradiction with them being alongside his actual properties. The fact that Metaphysician Undercover talks about them as if they were other actual properties introduces a problem that is not really there.

Well, when it is a possibility, we cannot say that the predication is made — Metaphysician Undercover

Why not?

religion developed as a by-product of theory of mind. — Questioner

Sure, why not. I do not see why God could not work by natural means, in addition to supernatural means, to help us know what He is thinking.

Thanks.

Frank, Kripke's use of rigid designators is not discussed in the SEP article according to Banno. Would you object if we hear from Richard B's critique of rigid designators in this thread anyways?
— NotAristotle

That's fine. — frank

I think now is a good time to hear your critiques whenever you are ready Richard B.

Frank, Kripke's use of rigid designators is not discussed in the SEP article according to Banno. Would you object if we hear from Richard B's critique of rigid designators in this thread anyways?

Sure, but as I said, with possible worlds we are talking about different properties at the same time. That is what prevents the name from referring to the same thing. — Metaphysician Undercover

We are talking about possible "properties" of a thing, the referent, in this case "Nixon." Insofar as those properties are merely "possible" I don't see why they can't be attributed to Nixon, even at the same time, as Nixon's actual properties.

Thanks for your thorough comments earlier. I am afraid I cannot do it just with a similarly thoroughgoing reply.

I do not really have any reason to argue against what you have said. However, I do want to phone-in on this assertion:

When we talk about what is possible, we are not talking about a set, namely the set of all possible things. — Leontiskos

I am unsure whether a possible world semantics interpretation of modal logic can still be extensional if it refers to, not only currently existing things, but in addition, "possible things."

To Metaphysician Undercover's point, we might wonder whether a "black frog" refers to anything if its existence is limited to something like possible worlds. And yet, if we consider all the existing frogs, that is what I take us to be referring to if we were to list all the things that fit into the domain for the predication "black frog." It is the property "black" that is "possible" not the referent, which is all extant frogs, now existing, and all of which could be black. On the other hand, perhaps imaginary things like "Frosty the Snowman" can be referents too; but of that I am less certain. In terms of just intension, it is clear that "Frosty the Snowman is a holiday character, but I am less certain whether Frosty is extensional in the sense of having a referent. All that said, I think possible world semantics definitely works extensionally, at least when the referents are well-defined in the actual world.

Since the properties of the thing named "Nixon" in this case, are different in the different possible worlds, we cannot say that there is a single referent, — Metaphysician Undercover

This is what you said. But you presumably also agree that the same thing can have different properties over time. If the same thing can have different properties over time, then the same thing can have different properties and still be the same thing. Therefore, different possible attributes of Nixon can refer to the very same Nixon, as would be the case whether Nixon was actually fat or actually skinny.

EDIT: Or put another way, the fact that different possible Nixons have different properties does not render them different Nixons.

negatory Banno, not too much, the lingo is :up: :up:

extensionality lost = no referent for modal logic claims. "Necessarily all John's pets are mammals" is false, but because there is no extension to corroborate the falsity; that is, there is only Algo and Basic in the set satisfying the predicate "all John's pets" it appears that maybe the statement should be true. At least then substitution would be preserved.

However, I think "all John's pets" in the statement "necessarily all John's pets are mammals" means all John's possible pets. Thus the semantic interpretation of the modal claim. Extensionality regained = all John's possible pets are the referents of the expression "John's pets" in the statement "Necessarily all John's pets are mammals."

Since the properties of the thing named "Nixon" in this case, are different in the different possible worlds — Metaphysician Undercover

The same thing cannot have different properties at different times?

Why would God be responsible for the actions of another agent? That is, why does creation entail responsibility for the actions of another?

Here is a thought experiment: would parents be morally responsible for their adult child's actions if they foresaw, but did not will or cause, that the child would do something morally wrong? If so, why are they morally responsible for another agent's free actions?

Saying "god did it" or whatever just kicks the can down the road; the same explanatory gap would exist for God. — Mijin

I agree with you that eternity itself is not an explainer.

My understanding of Aquinas is that: even if the universe itself is eternal, if anything in the universe (e.g. movement, causation, generated beings) requires a first member, then there would be an explanatory gap for those elements of the universe if not for God.

I think material things can arise out of nothing material, but something cannot come out of absolute nothingness.

His point was that the intensionality of modal logic is irrelevant to the fact that possible world semantics establishes extensionality by predicates having different individuals in their domains depending on the possible world, and that it is this difference that defeats substitutivity for modal logic. At least I think that is correct.

But i think Banno was not making the claim that modal logic is not intensional.

1.1 -> "Modal logic, by contrast, is intensional."

predicate extensions vary from world to world. — Banno

And consequently sentence extensions; that is, truth value, also varies across worlds.

Your objection against possible worlds makes sense to me. Extensionality seems to require a referent of some sort; and I am not sure the article has defended any such referent up to now.

Kripke postulates "rigid designators," I think. So if Nixon is the referent of the term "Nixon" in any given possible world, maybe that alone solves extensionality without having to worry about the existence of "possible worlds." What do you think?

T Clark -- "Okay everyone, who wants to test out this wooden bridge I designed?" "I designed it within 6 orders of magnitude so it will either hold all of you or collapse immediately."

"No thanks."

optimistic NotAristotle "Sure! I'm sure it'll be fine."

Did you want to design bridges?

Chatgpt flubbed then — Mijin

Yeah, it was Chatgpt, the machine that is built to say smart things, that's probably who messed up in this situation.

I don’t know what you’re complaining about — T Clark

I'm not complaining.

I agree with your following quotes about biological ETI:

" the more rigorously we've observed the non-terrestrial universe the less we find non-terrestrial exotica "out there" as the same physics & chemistry which apply here more & more apply everywhere that we can observe"

"I can't imagine that other celestial objects made up of sufficiently chaotic physical & chemical systems-processes don't give rise to their own particular biological histories (i.e. evolutionary paths), of which some are, at least, as robust as Earth's."

"It seems to me that everything we're learning about the universe reasonably points in the direction of the non-uniqueness (though perhaps not "ubiquity") of biological phenomena however sparsely distributed throughout the universe."

Do you think the biological process necessarily leads to sapience in all cases; if so, what are your reasons?

I have literally never called the police in my entire life. Not once. — AmadeusD

:lol:

:clap:

Well, how long does think ETI could survive and does he think we can make it that long?

Define "our reality." Who is us and how is "real" defined?

Based on T Clark's assertion that 1 million years for ETI to survive is "wildly optimistic" and that he "doubts we'll be around that long" I have to agree that he seems a bit pessimistic about the whole alien contact situation.

Strikes me as wildly optimistic. I doubt we’ll be around that long. Make it 10 million years and it doesn’t really change the situation much. — T Clark

Okay. Yeah, I was curious why an advanced alien race would decide to call it quits at the 1 million year mark. I do not think it is "wildly optimistic" however. Why do you think we won't make it that long?

Assuming every intelligent civilization lasts for 1 million years — T Clark

Wait, what happens after 1 million years? :sweat:

What I learnt from your responses in this thread is that most of you are pessimistic on the probability of a possible contact. — javi2541997

I do not think anyone is saying that. And pessimistic is definitely the wrong word.

The words "necessarily" and "possibly" do not denote extensional sets. — Leontiskos

Can you say what you mean by this?

Do you mean a sentence with these terms cannot have a truth value, or do you mean they fail at substitutivity always?

So I think a key parameter in making a probability calculation is the similarity of these other billion worlds to Earth. My understanding is: what is used is the ESI (Earth Similarity Index). https://en.wikipedia.org/wiki/Earth_Similarity_Index . This index looks at features like the size of the planet. But it really does not tell us the planet composition nor whether it has a magnetosphere; a lot of information appears to be missing to say if it is really "like" Earth. So if we cut out a large percentage of those sort-of-Earth planets then there are perhaps far fewer than a billion planets that could, (or that we would expect) to host life.

That is not to mention that our planet was hit by an asteroid (or meteor?) that wiped-out the dinosaurs and arguably paved the way for the emergence of intelligent life. So while life may be a more likely occurrence on a planet that is similar to Earth in key respects, intelligent life may be far more rare.

And how would we determine that they aren’t visiting, or even aren’t here now? — Tom Storm

You may be interested to read Sagan's article on interstellar diffusion/propogation: https://ntrs.nasa.gov/api/citations/19790011801/downloads/19790011801.pdf . There are more recent articles too that have narrowed down the estimate for galactic colonization based such factors as the rotation of star systems in the galaxy.

For me the Fermi paradox loses a lot of it's argumentation, when one takes into account that the first radio signals we have ever sent to space have reach only a tiny spec even in our own galaxy. Add then the fact that radio signal get weaker when the ranges get longer. — ssu

Agree. Any ETI that formed around the time we did and that sent out radio signals within the past century or so would take a long time to even reach us (10s of thousands of years).

there has been ample time for thousands of species to have made noise detectable to us. — Mijin

I think this claim may be contested. We really just may not know how rare planets similar to Earth are, life is, or ETI is.

:up: Got it.

Yeah I am still confused about why modal logic itself is not extensional, but possible world semantics is apparently extensional.

I see. I think my questioning about semantics in relation to logic was in reference to propositional logic that deals with formal languages only; in that case, maybe you would see why I would wonder how semantics fits. But I understand how an interpretation can add a semantic component to predicate logic.

we need a semantics, an interpretation of the symbols. — Banno

By this I understand you to be saying that the symbols need to refer to something (or predicate something) in the world (or in a possible world if we are using possible world semantics).

And that is because there is no way of making sense of "necessarily" under a Tarskian interpretation and without possible world semantics.

That is, the sentence: "Necessarily, all John's pets are mammals" is not a sentence that can be parsed by a Tarskian interpretation that converts the first order logic to that sentence.

Alright, then by statement do you mean a token of some proposition in some possible world?

Why is that? — frank

I was thinking it is because the Tarskian interpretation of the extension(s) referenced by a quantifier does not account for possibility.

haha, yeah I was thinking that myself, and I think it is a good question. It would seem to have to do with the evolution of that species and how risk adverse they are, or perhaps, with how communicative they are. If they are less communicative and more cautious like (I don't know turtles hiding in a shell?) then maybe they will refuse to broadcast any signals. Of course, if nobody broadcasts then the chance of any communication plummets.

Walk me through better to not have crossed paths; why would that be so?

1.2

The problem we ran into with the extensionality of modal logic concerned the fact that modal logic appeared to not be subject to classical substitutivity principles. An ostensibly more accurate statement would be that classical substitutivity does not hold when first order logic Tarskian interpretation is attempted to be translated into modal logic's possible worlds interpretation.

A Tarskian interpretation appears to apply only to the actual world. Thus, the author says that the Tarskian interpretation: "fixes the domain of quantification and the extension of all predicates." Tarskian interpretation, with its own semantics, does not appear to allow for possibility. That is why a possible world semantics was proposed for modal logic.

To try to simplify some of the symbolism in the article, the "possibly" quantifier: quantifies over a set of statements that themselves refer to states of affairs that are true about at least one possible world (w). The "necessarily" quantifier: quantifies over a set of statements that refer to states of affairs that are true of the set of all possible worlds (u).

It seems to me that substitutivity principles can be maintained within a possible world semantics applied to modal logic, but that a Tarskian interpretation of first order logic cannot be reconciled with possible world semantics.